NEW INSTRUMENTS AND METHODS OF MEASUREMENT

APPLICATION OF RADIOACTIVE ISOTOPES IN ANALYTICAL CHEMISTRY

M. B. Neiman and V. B. Miller

Along with the wide use of radioactive isotopes in industry, biology, medicine, and inorganic, organic, and physical chemistry, they are also often used in analytical chemistry for carrying out routine analyses and for solving a number of problems in scientific research. Below we shall briefly consider the principal directions in the application of radioactive isotopes in analytical chemistry, dividing the material into three sections: physical methods of analysis, chemical methods of analysis, and the application of radioisotopes in research work.

A. PHYSICAL METHODS OF ANALYSIS

In this section we shall consider those methods of carrying out analyses in which only physical measurements are used and physical manipulations are performed, without applying chemical separation of substances and without any other chemical operations.

1. Determination of Elements Possessing Natural Radioactivity

A large number of natural elements (Ra, Rn, U, Th, etc.) located at the end of Mendeleev’s periodic system of elements, as well as some elements with lower molecular weight (K, Rb, Sm, and others), possess natural radioactivity and decay, emitting α- and β-particles. With the aid of an ionization chamber, counters, or radiography it is possible to determine these elements in the substance under investigation qualitatively and, in many cases, quantitatively as well. The determination of radium and radium emanation from the ionization they produce is widely known.^1

In recent years a method has been developed and introduced into practice for the quantitative determination of potassium by registering the \(\beta\)-particles emitted by the isotope \(K^{40}\). This isotope, present in natural potassium in an amount of \(0.011\%\), has a half-life of \(1.3 \cdot 10^9\) years and a maximum \(\beta\)-particle energy of \(1.36\) MeV. As has been shown by a number of investigators \(^{2,3}\), samples containing potassium, with a thickness exceeding \(0.4\ \mathrm{g/cm^2}\), are characterized by constant radiation independent of thickness. In this case the count rate of the sample is, over wide limits, directly proportional to the concentration of potassium in it. A calibration curve for the determination of potassium is shown, for example, in Fig. 1, taken from the work of Godin \(^{2}\). In recording this calibration curve the authors used a thin-walled cylindrical counter, onto which a hollow thin-walled vessel was slipped, filled with the dry powder whose potassium content was to be determined.

Naturally, the thickness of the potassium layer in this case considerably exceeded \(0.4\ \mathrm{g/cm^2}\), which made it possible to dispense with a correction for self-absorption. It is clear that different chemically pure substances containing potassium in different amounts—for example the salts \(KClO_3\), \(KCl\), and \(KMnO_4\)—must have different radiation intensities corresponding to their percentage potassium content. Such a relation is clearly visible from Fig. 2.

Of great practical importance in the radiotechnical industry is the quantitative determination of thorium content in tungsten wire. A rapid and convenient method for determining small admixtures of thorium in tungsten by radioactive radiation was developed by Mikhaleva \(^{4}\). She designed a special counter with a hollow nickel anode whose wall thickness was less than \(0.1\) mm. If thoriated tungsten is inserted inside the hollow anode, the counter registers, above background, a number of pulses proportional to the thorium content in the tungsten. The author, who used this new sensitive method, succeeded in showing that the thorium concentration in individual sections of wire containing on average \(1.1\%\) thorium fluctuates over wide limits. In the table given on p. 96, a number of the author’s determinations are compared, obtained as a result of radiometric measurements of separate sections of a 55-meter wire.

Natural radioactivity, as indicated above, can also be determined by the method of radiography. This method for determining the content of small amounts of radium—on the order of \(10^{-11}\) g—in plants was recently developed by Drobkov \(^{5}\). According to this method, a plant containing traces of radium is pressed against the light-sensitive layer of a photographic plate. After the appropriate exposure the photographic plate is developed, and its blackening will be greater in those places near which higher concentrations of radium had been distributed.

Fig. 1. Calibration line for the determination of potassium.

Fig. 2. Radiation intensity of various potassium salts:
\(1\) — \(\mathrm{KClO_3}\), \(2\) — \(\mathrm{KCl}\), \(3\) — \(\mathrm{KMnO_4}\).

Drobkov grew clover, peas, and several other plants in water cultures containing traces of radium. The negative image of the radiograph of pea leaves obtained by this author, on which blackenings are clearly visible opposite the places with a higher concentration of radium, is presented in Fig. 3. In positive prints similar to the radiograph of clover shown in Fig. 4, the places with a higher concentration of radium correspond to white areas.

Table I

Determination of thorium in tungsten wire

Fig. 3. Negative image of the radiograph of pea leaves.

Photometering the blackening of negatives exposed and developed under standard conditions makes it possible, as the author asserts, to carry out a quantitative determination of the content of radium and other radioactive elements in plants.

In conclusion to this section we would like to note that a research associate of Moscow University, V. I. Spitsyn, in 1917 was the first to apply widely the method of measuring natural radioactivity for investigations in the field of analytical chemistry.^6,7

2. Emanation Method

Uranium, radium, thorium, actinium, and a number of other elements possessing natural radioactivity form, in the process of decay, radioactive gases—radon, thoron, and actinon. If radioactive equilibrium has been established in the samples under investigation, then, removing the above-mentioned gases from them and determining their radioactivity with the aid of an $\alpha$-counter or an electrometer, one can calculate the content in the samples of radium, thorium, and some other elements. This procedure, often used for the determination of natural radioactive elements, is called the emanation method.

Kolowrat-Czerwinsky, about 35 years ago, developed and widely applied a method of isolating radon from fused salts for determining the content of radium in them.^8

Khlopin and Pasvik, in their investigations of the migration of radium, developed an emanation method for determining radium in aqueous solutions.^9

Fig. 4. Positive image of a radiograph of clover.

The authors of the cited work first dissolved the samples, precipitated barium and radium in the form of sulfates, and converted radium

into solution by fusion of the sulfates with soda. Then the emanation was blown out of this solution with a stream of air and its activity was determined with an electrometer.

The method of determining thorium from thoron was developed in detail by Baranov[^10].

The apparatus used by this investigator is shown schematically in Fig. 5. The solution whose thorium content is to be determined is placed in flask 1. Air blown through this solution carries the thoron with it into dryer 2, whose volume is \(v_1\), and into ionization chamber 3 (its volume is \(v_2\)). The current \(I\), determined by electrometer 4, is related to the amount of emanation \(E\) liberated per unit time and to the volume rate of flow of air \(\omega\) by the equation

Fig. 5. Schematic of the apparatus for determining thorium by the emanation method. 1 — flask with a solution of thorium salts; 2 — dryer; 3 — ionization chamber; 4 — electrometer.

\[ I=kE\left(e^{-\frac{\lambda v_1}{\omega}}-e^{-\frac{\lambda(v_1+v_2)}{\omega}}\right). \tag{1} \]

Here \(\lambda\) is the decay constant, and \(k\) is a constant depending on the design of the instrument.

If the current \(I\) is measured as a function of the rate of air blowing \(\omega\), a curve with a maximum is obtained, as shown in Fig. 6.

Equating the derivative \(\frac{dI}{d\omega}\) to zero, it is easy to find the value \(\omega_{\max}\) corresponding to the maximum current. By setting the air-blowing rate to

\[ \omega_{\max}=\frac{\lambda v_2}{\ln\frac{v_1+v_2}{v_1}}, \tag{2} \]

one can ensure the maximum sensitivity of the determination of thorium.

Helmick[^11] compared the method of determination by thoron with the gravimetric method of determining thorium in monazite sands. It turned out

It turned out that the discrepancy usually does not exceed 2%, but the emanation method requires much less time.

A detailed description of the apparatus used for determinations by the emanation method may be found in the paper by Evans\(^{12}\).

Fig. 6. Dependence of the ionization-current strength \(I\) on the rate of blowing air \(\omega\).

Various applications of the method are described in Curie’s monograph\(^{13}\) and in the recently published article by Baranov, Zaborenko, and Nesmeyanov\(^{14}\).

3. Simultaneous determination of two radioactive elements differing in radiation energy

In many cases, when it is necessary to determine the content of two radioactive isotopes in a sample, this can be done if they possess markedly different radiation energies.

We encountered a similar problem in determining the products of the reaction of chlorine with neutrons. As is known, in this case, by the reactions

\[ \mathrm{Cl}^{35} + n = \alpha + \mathrm{P}^{32}, \]

\[ \mathrm{Cl}^{35} + n = p + \mathrm{S}^{35}, \]

the isotopes \(\mathrm{P}^{32}\) and \(\mathrm{S}^{35}\) are obtained, with half-lives of 14.3 days and 87 days. Measuring the total activity with the aid of an end-window counter with a thin mica window, we obtained the dependence of the activity \(I\) on the amount of products, represented by line 1 in Fig. 7.

For the separate determination of phosphorus one may take advantage of the fact that the energy of the \(\beta\)-particles emitted by it, 1.7 MeV, is many times greater than the energy of the \(\beta\)-particles of sulfur (0.17 MeV). If the measured sample is covered with a sheet of aluminum 0.1–0.2 mm thick, then

the radiation of sulfur will be absorbed completely, whereas the β-particles of phosphorus will pass through the screen almost 100%. The calibration curve obtained in the presence of the screen is also shown in Fig. 7. It is clear that from line 1 one can determine the phosphorus content, and from the difference between lines 1 and 2—the sulfur content. Of course, in doing so it is necessary to introduce corrections for self-absorption, counting losses, etc.

Fig. 7. Calibration curves for determining \(S^{35}\) and \(P^{32}\). Curve 1 corresponds to the total activity of \(P^{32}\) and \(S^{35}\), curve 2 to the activity of \(P^{32}\) alone.

In an analogous manner one can carry out the simultaneous determination in a sample of the isotopes \(I^{131}\) and \(P^{32}\). In this case it is necessary to select a screen of such thickness as to stop completely the β-particles of iodine (0.6 MeV) and phosphorus (1.7 MeV) and to transmit practically completely the γ-radiation of iodine. Iodine is determined from the latter radiation, and phosphorus from the difference.

Recently a method\(^{15}\) was developed for the simultaneous determination in samples of \(Na^{24}\) and \(K^{42}\), which have different maximum β-particle energies: 1.39 and 3.58 MeV, respectively. These isotopes also emit γ-quanta of different energies. With the aid of a specially selected screen it proved possible to establish the determination of the indicated elements with an accuracy of 3.5%. It should be noted that the very laborious gravimetric determination of sodium and potassium requires no less than 12 hours, whereas the radiometric method makes it possible to obtain results within 10–15 minutes.

4. Separate determination of two radioactive isotopes by analysis of decay curves

In some cases it is possible to determine two radioactive isotopes separately by making use of the difference in their half-lives. We encountered such a case in determining the isotopes \(K^{42}\) and \(Ca^{45}\) in samples. The first of them has a half-life of 12.4 hours, and the second—152 days. Observing over the course of

Fig. 8. Separate determination of \(K^{42}\) and \(Ca^{45}\) by analysis of the total decay curve. 1—the total decay curve of \(Ca^{45}\) and \(K^{42}\), 2—decay of \(K^{42}\), 3—decay of \(Ca^{45}\).

Fig. 9. Separate determination of Al (2.3 min.), Mn (2.6 hours) and Na (14.8 hours) by analysis of the total decay curve.

100 hours the decay curve shown in Fig. 8 in semilogarithmic coordinates, we were able to decompose this curve into two components 2 and 3, shown in the same figure. The slope

line 2 corresponds to the half-life of \(K^{42}\), and line 3 to the half-life of \(Ca^{45}\). By extending these lines to their intersection with the ordinate axis, one can determine the activities and, consequently, the amounts of both radioisotopes at the initial instant of time.

If the half-lives differ greatly, analysis can also be carried out in more complicated cases, when the mixture contains three or even more radioisotopes. As an example one may cite the method developed by Boyd\(^ {16}\) for determining manganese and sodium in aluminum.

The decay curve reproduced in the cited work and shown in Fig. 9 can readily be resolved into three components, whose slopes correspond to the half-lives of aluminum (2.3 min), manganese (2.59 hr), and sodium (14.8 hr). The content of manganese and sodium in aluminum can be determined as indicated above.

5. Determination of Radioisotopes from \(\alpha\)-Tracks in Photoemulsion

The method of thick-layer emulsions, introduced by Mysovskii\(^ {17}\) and improved by Zhdanov\(^ {18}\), is now widely used in nuclear physics and is an indispensable means of investigating cosmic rays, mesons, and various nuclear reactions.

This method has also found application in analytical chemistry for determining small amounts of uranium and thorium when they are present together. If an extremely thin layer of a substance containing uranium, which is in equilibrium with the other members of the family, is placed on a thick-layer photographic emulsion, then \(\alpha\)-particles produced in the decay of UI, UII, Io, Ra, and other members of the series will enter the photoemulsion. The ranges of these particles in the photoemulsion, according to the Geiger–Nuttall rule, are related to the half-lives of the corresponding elements. If, after a sufficient exposure, chosen as a function of the uranium concentration in the substance, the photographic plate is developed, then, when it is examined under a microscope at high magnification, tracks of \(\alpha\)-particles of different lengths are visible.

As a result of measuring several hundred tracks, it is easy to calculate the probability distribution for finding a track as a function of its length. The curve thus obtained for uranium differs from the analogous curve for thorium, the members of whose family are characterized by different ranges.

Construction of the curve obtained by such a method for an unknown specimen makes it possible not only to conclude that uranium and thorium are contained in the specimen, but also to determine the relative amounts of these substances. Counting the tracks of \(\alpha\)-particles in thick-layer emulsions is greatly facilitated if stereoscopic photographs of a group of tracks are examined.

The development of such a procedure was carried out and described more than 20 years ago\(^ {19}\).

6. Activation Analysis

About 12 years ago A. A. Grinberg[^21] proposed determining the content of iridium in platinum by the method of neutron irradiation of the sample. In this, as Grinberg showed, owing to the large cross section of iridium it is possible easily to detect an iridium content of 0.1% in platinum. The latter is quantitatively determined from the activity of the isotope \( \mathrm{Ir}^{194} \) formed. This method of analysis, introduced into science by Grinberg, subsequently received the name of activation analysis. In recent years activation analysis has become widespread and is known in several variants.

The most common type of activation analysis is associated with irradiating the substance being analyzed with slow neutrons. In this case isotopes with large cross sections can be determined at extremely low concentrations. By this method Brown[^22] and Goldberg[^23] determined negligible contents of gallium, gold, palladium, and rhenium in meteorites (\(10^{-5}—10^{-6}\%\)). Other authors[^24] determined neodymium, praseodymium, and cerium in a mixture of rare earths. Tobashi and co-workers[^25] developed activation analysis of gold in animal tissues. In this case the sensitivity of the determination is \(10^{-5}\%\). The high sensitivity of the analysis is to a considerable extent explained by the use of powerful neutron fluxes from a uranium reactor. Recently this method has often been applied in practice for determining arsenic in germanium[^26], hafnium in zirconium, indium in tin, tantalum in niobium, and coatings of gold, silver, cadmium, and rhodium[^27].

Activation analysis makes it possible in a number of cases to determine the isotopic composition of an element. Such an application of activation analysis is based on the difference between the absorption cross sections of slow neutrons by different isotopes, and also on the difference in the half-life times and radiation energies of the isotopes formed.

As an example one may cite the analysis of chlorine, which, as is known, consists of a mixture of the isotopes \(\mathrm{Cl}^{35}\) and \(\mathrm{Cl}^{37}\). The cross sections of these isotopes are equal to \(\sigma_{35}=0.17\cdot 10^{-24}\ \mathrm{cm}^{2}\) and \(\sigma_{37}=0.56\cdot 10^{-24}\ \mathrm{cm}^{2}\). The isotopes \(\mathrm{Cl}^{36}\) and \(\mathrm{Cl}^{38}\), formed upon neutron absorption, have half-lives of \(4.4\cdot 10^{5}\) years and 38 minutes and maximum β-particle energies \(E_{36}=0.7\ \mathrm{MeV}\) and \(E_{38}=4.9\ \mathrm{MeV}\).

It is clear that the determination of chlorine by neutron activation, developed by Dolezal[^28], is based on counting the β-particles emitted by the isotope \(\mathrm{Cl}^{38}\), since the activity of the isotope \(\mathrm{Cl}^{36}\) is negligibly small.

It is obvious that activation analysis can be successfully applied to controlling the enrichment of chlorine with a heavy isotope, for example in the thermodiffusion method of separating chlorine isotopes. Undoubtedly, one of the promising applications of the activation method of analysis in the future will be its use for monitoring isotope separation.

Another type of activation analysis is also frequently used; in its implementation the substance under investigation is bombarded with deuterons, protons, or $\alpha$-particles in a cyclotron or an accelerator of another type. As an example of this type of analysis one may cite the method developed by Ardenne$^{29}$ for determining carbon in iron. The short-lived nitrogen isotope $\mathrm{N}^{13}$, obtained under deuteron or proton bombardment by the reactions

\[ \mathrm{C}^{12}_{6}+\mathrm{H}^{1}_{1}=\mathrm{N}^{13}_{7}+\gamma, \]

\[ \mathrm{C}^{12}_{6}+\mathrm{H}^{2}_{1}=\mathrm{N}^{13}_{7}+\mathrm{n}^{1}_{0}, \]

emits positrons with an energy of $1.24\ M_{e}v$. The resulting activity is measured on a counter and compared with the activity of standards with a known carbon content.

The irradiation was carried out on a Van de Graaff installation at a voltage of 800 kv. Delivery of the samples for analysis from production was carried out by means of pneumatic mail. With quite satisfactory accuracy, the analysis, including irradiation, took only 15 minutes in all.

A substantial advantage of activation analysis is the circumstance that this method makes possible the analysis of finished articles and parts without damaging them.

7. Analysis by neutron absorption

An extremely elegant variety of physical methods of analysis is analysis by neutron absorption. By this method it is possible to determine, in the substance under investigation, the content of certain elements with large absorption cross sections. The method of absorption of slow neutrons can be used, for example, to determine boron in glass$^{30}$. The apparatus used for this purpose is shown schematically in Fig. 10. In this case a radium-beryllium source placed in paraffin was used as the neutron source,

Fig. 10. Diagram of an installation for the quantitative determination of boron in glass. $A$ — detector, $B$ — glass under test, $C$ — neutron source, $E$ — cadmium shielding.

block. The neutrons slowed by paraffin pass through a layer of glass and enter a dysprosium neutron detector. It is clear that, with an increase in the boron content in the glass, an ever greater number of neutrons will be absorbed by the reaction

\[ {}^{10}_{5}\mathrm{B}+{}^{1}_{0}\mathrm{n}={}^{4}_{2}\mathrm{He}+{}^{7}_{3}\mathrm{Li}, \]

and consequently the activation of the detector, associated with the formation of the radioisotope \( \mathrm{Dy}^{165} \), will decrease. If, using a set of glass standards containing different amounts of boron, the corresponding activities of the \( \mathrm{Dy}_{2}\mathrm{O}_{3} \) neutron detector are measured, it is easy to construct a calibration curve for determining the boron content in glass samples.

In the case of using neutron absorption for analysis, neutron indication can be carried out not only by means of various detectors, but also by means of neutron counters filled with boron trifluoride. Such an apparatus for determining the boron content in boron carbide was described by Walker^31. A diagram of this apparatus is shown in Fig. 11. A radium–beryllium source is placed in a paraffin block. Into the same block there may be inserted a vessel containing

Fig. 11. Diagram of an apparatus for the quantitative determination of boron in boron carbide.
1 — paraffin, 2 — neutron source, 3 — lead, 4 — neutron counter, 5 — suspension of boron carbide under investigation.

finely ground boron carbide mixed with water. The flux of slow neutrons that has passed through the suspension of boron carbide enters counter 4. It is clear that the readings of the neutron counter decrease with an increase in the boron content in the boron carbide.

The physical methods of radiometric analysis considered above, owing to their simplicity and speed, will undoubtedly in the future be applied more and more widely in research work and for the control of production processes.

B. CHEMICAL METHODS OF ANALYSIS

Radiometric methods can be successfully used in combination with chemical methods for the separation and determination of individual components.

1. Chemical separation with radiometric control

In some cases, after separating a mixture into components by the precipitation method, it is advisable to determine the amounts of the individual constituents not by weighing, but by determining the activity of the precipitates. This procedure leads to a significant reduction in the duration of analyses and may be recommended in those cases where a relative accuracy of determinations on the order of 2–3% may be considered satisfactory.

Such a method of work should be especially recommended when one has to deal with extremely small amounts of substances with a high and known content of radioactive isotopes. In this case, before the chemical separation, a certain amount of carrier is added to the mixture.

As an example, one may cite determinations of phosphoric acid, containing a known amount of the radioisotope \(P^{32}\), that have been performed many times in our laboratory. From a complex solution the phosphoric acid was precipitated by the molybdate method, after which the activity of the precipitate was determined with the aid of a counter. From the magnitude of the activity and the known specific activity of phosphorus, the content of the \(PO_4^{---}\) ion in the solution was determined. This analysis, with an error not exceeding 3%, took about 20 minutes.

A method for determining small amounts of strontium and barium in mixtures was developed in 1950 by Miller, Dzantiev, and Neiman in our laboratory during a study of the evaporation process of SrO and BaO. Barely perceptible deposits of SrO and BaO, formed as a result of condensation of the oxide vapors, were dissolved in nitric acid, after which 15 mg each of strontium and barium salts were added to the solution as carrier. Barium was then precipitated as \(BaCrO_4\), and strontium from the filtrate as \(SrSO_4\). From the activity of the precipitates, the content of barium and strontium in the deposits formed by evaporation of their oxides was determined.

Recently, Leverton and Shepert \(^{33}\) essentially reproduced our results; moreover, they were forced to carry out a large number of experiments, since they did not cope with the solution of the problem of the chemical separation of the alkaline-earth metals.

In the literature of recent years, many cases have been described of the determination of radioactive isotopes in practically unweighable amounts, carried out by similar methods \(^{33, 34}\).

Chemical separation can be achieved not only by precipitation, but also by other methods. Thus, Henriques and Margnetti^35 found the concentration of arsenic by reducing it to the metal, with subsequent determination of the activity of the metallic mirror. The literature also describes methods for isolating various components of a mixture by evaporation, electrodeposition, and with the aid of other procedures. In all these cases the final stage of the analysis is the determination of activity.^36

2. Distillation with Radiochemical Control of Fractions

Distillation methods at high, medium, and low temperatures are used in laboratory investigations, and also in a number of branches of industry. The progress of distillation is usually monitored by chemical or physicochemical analysis of individual fractions.

Recently it was proposed to monitor the composition of distillates by a radiometric method.^37 In a number of cases radiometric control has proved much more economical than the classical methods previously used. In cases where it is necessary to distill organic substances that are similar in their properties and whose chemical analysis is very difficult, the radiometric method is indispensable. Such a case may be encountered in the distillation of multicomponent mixtures of hydrocarbons, alcohols, or acids with similar physicochemical properties. By adding to the mixture small amounts of individual compounds containing radioactive carbon in the molecule and determining the activity of the individual fractions, it is easy to monitor the operation of the distillation column.

Having prepared labeled \( \mathrm{C}^{14}\mathrm{H}_3\mathrm{OH} \), Hughes and Maloney^38 were able to determine the pressure and composition of the vapor of the ternary system—methyl alcohol, ethyl alcohol, and water—and also to monitor the distillation of this mixture.

There can be no doubt that, in the future, the labeled-atom method will find still broader application in the investigation and control of evaporation and distillation processes.

3. Radiometric Control in Chromatography

The chromatographic method, introduced into science by M. S. Tsvet^39, is now widely used in the analytical chemistry of inorganic and organic substances. In its classical form this method amounts to introducing a solution of the substances under investigation into a tube filled with a suitable adsorbent. When the adsorbent is eluted with an appropriate solvent, the substance being analyzed is separated in the column into a number of components located in different zones. If the individual components of the mixture are colored, then their location

is detected with the naked eye. Continuing the elution, it is possible to wash out of the column, one after another, all the components and collect their solutions in different vessels. In the case of work with uncolored components, determining their location in the column is a more difficult task. It can be solved by observing fluorescence in ultraviolet light according to Brumberg^40 and by several other methods. One of the most general methods amounts to the use of radioactive indicators in chromatography. This method has yielded results of extraordinary importance, both theoretically and practically.^41,42

Fig. 12. Diagram of an apparatus for the separation of rare elements on a chromatographic column using a counter for indicating the components. \(B\)—column filled with adsorbent, \(C\)—rotameter, \(D\)—counter, \(E\)—lead shield, \(K, I, H\)—system of amplifiers and regulators.

Radioactive isotopes of the elements to be separated are added to the mixture and introduced into the column, as is shown schematically in Fig. 12. The solution issuing from column \(B\) during elution at a constant rate passes through rotameter \(C\) and through the spiral surrounding counter \(D\), protected by lead shields \(E\).

At those moments when one of the components of the mixture being separated passes through the spiral, the counter sends pulses into the system of amplifiers and recorders \(K, I, H\). In Fig. 13, as an example, one of the curves obtained on such an apparatus^43 in the separation of a complex mixture of rare-earth elements is shown.

Using the readings of the counting apparatus, it is possible to direct individual fractions of the solution flowing out of the column into different receivers and thus to solve, comparatively simply, the problem of separating rare-earth elements—

Fig. 13. Curve obtained in the separation of rare elements on the apparatus shown in Fig. 12.

—a problem which, by other methods, could be solved only at the cost of incomparably greater labor.

Radioactive isotopes are also used with great success in paper chromatography. Thus, Neiman, Lukovnikov, and Levkovskii^44 used paper chromatography to separate various aldehydes and acetone containing the radioisotope C^14 in the molecule. Fig. 14 schematically shows the chromatogram obtained by these authors, on which spots corresponding to the dinitrophenylhydrazones of formaldehyde and acetaldehyde, as well as to the osazone of glyceraldehyde, are clearly distinguished.

Fig. 14. Distribution chromatogram of aldehyde dinitrophenylhydrazones. Mobile liquid—ethyl alcohol. \(T = 40^\circ\)C. Hydrazones of formaldehyde (\(a\)), acetaldehyde (\(v\)), and mixture (\(b\)).

Paper chromatography was also applied by Benson and Calvin^45 to separate a complex mixture of organic compounds obtained during photosynthesis in an atmosphere containing \(C^{14}O_2\). The authors pressed their two-dimensional chromatograms against photographic film and, after prolonged exposure and development, observed blackening in those places on the photographic film opposite which the radioactive products of photosynthesis had been located.

4. Method of isotopic dilution

In cases where quantitative separation of the components is difficult, but it is relatively easy to isolate a small portion of each component in pure form, the method of isotopic dilution is used for quantitative analysis. The most widely used variant of this method amounts to introducing into the mixture \(a\) grams of the component being determined, with known specific activity \(p\). After thorough mixing, \(b\) grams of this component are isolated from the mixture and the activity \(k\) of this quantity is determined with a counter. The new specific activity of the substance under study,

\[ q=\frac{k}{b}, \]

is less than the specific activity \(p\) of the substance introduced, in the dilution ratio

\[ \frac{a}{x}, \]

where \(x\) is the desired quantity of the substance in the mixture. It is clear that

\[ x = a \frac{p}{q} = a\frac{bp}{k}. \tag{3} \]

If it is necessary to determine several substances, then weighed portions of all the substances to be determined, with known specific activities, are added to the mixture. Having isolated small quantities of these substances in pure form and determined their specific activities, the content of these substances in the mixture is calculated by the above formula.

Acting in a similar way, Henriques and Margnetti\(^ {46}\) determined, in a mixture, dibenzyl sulfide, dibenzyl sulfoxide, and dibenzyl sulfone, using for isotopic dilution these same substances labeled with the radioisotope \(S^{35}\).

The method of isotopic dilution with a labeled component is often used in biological and medical investigations to determine the content of water and of a number of salts in intact organisms\(^ {47}\).

In recent years a method of reverse isotopic dilution has also been developed. It is used for the quantitative determination of traces of substances possessing a known high specific radioactivity. A definite amount of inactive substance to be determined is added to the sample being analyzed. Then part of this substance is isolated in pure form and its specific activity is determined. The desired amount of substance is found from the equation

\[ \frac{y}{a+y}=\frac{q}{p}, \tag{4} \]

where \(a\) and \(y\) are the added and the determined amounts of substance, and \(p\) and \(q\) are the initial and final specific activities of the substance. Solving equation (4), we obtain the formula for calculating the results of the analysis

\[ y=\frac{aq}{p-q}. \tag{5} \]

Dortem et al.\(^ {48}\), by the method of reverse isotopic dilution, determined \(\mathrm{CH}_3 I^{131}\) and \(\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2 I^{131}\), formed in small concentrations in the reaction of methyl and propyl radicals with radioiodine vapors. Thus, these authors succeeded not only in detecting the above-mentioned radicals during the pyrolysis of certain compounds, but also in showing how their concentration changes with changes in the temperature conditions.

5. Radiometric titration

One of the most widespread methods of using radioisotopes in analytical chemistry is the method of radiometric titration. For radiometric titration, solutions of substances labeled with long-lived radioactive isotopes, prepared for titration by the usual method, are used. Reactions associated with the formation of insoluble precipitates are used most simply for radiometric titration. The apparatus used for titration is shown schematically in Fig. 15. To the solution under investigation, located in a beaker, portions of the titrant solution containing a radioactive isotope are added; in the beaker an insoluble radioactive precipitate is formed. From time to time the titrated solution is sucked through filter \(B\) into the water jacket \(A\) of the counter. Having recorded the readings of the registering instrument \(C\), the titrated solution is poured back into the beaker and a further amount is added

quantity of solution from the burette. It is clear that only after the end of the reaction and the addition of an excess of reagent in the solution contained in the beaker does radioactivity appear, which is easily detected with the aid of a counter.

Langer[^49] used this method to determine the amount of halide ions in solution, titrating them with ions of radioactive silver. The titration curves obtained by him are shown in Fig. 16. Curve 1 corresponds to the addition of an Ag$^{110}$NO$_3$ solution to a NaCl solution,

Fig. 15. Diagram of the apparatus for radiometric titration.
A — liquid counter with external protection, B — suction tube with filter, C — mechanical counter.

Fig. 16. Curves of radiometric titration.
1 — titration of NaCl with an Ag$^{110}$NO$_3$ solution,
2 — titration of NaBr$^{82}$ with an Ag$^{110}$NO$_3$ solution,
3 — titration of Ag$^{110}$NO$_3$ with a NaBr solution.

curve 2 — to the addition of an Ag$^{110}$NO$_3$ solution to NaBr$^{82}$, and curve 3 — to the titration of Ag$^{110}$NO$_3$ with a NaBr solution.

In connection with the variety of known volumetric methods of analysis and the simplicity of the apparatus used for radiometric titration, this method is one of the most promising for routine determinations.

B. APPLICATION OF RADIOACTIVE ISOTOPES FOR THE DEVELOPMENT AND IMPROVEMENT OF ANALYTICAL METHODS

The method of labeled atoms in analytical chemistry is at present used mainly for scientific research work. Radioactive isotopes make it possible to determine the completeness of precipitation, solubility, to investigate phenomena of coprecipitation and adsorption, to study the aging of precipitates, and to determine a number of physicochemical-

chemical constants that are of importance in analytical chemistry. A number of works in this direction have been carried out by Soviet and foreign scientists.

It should be noted, however, that among the large number of works published abroad, only a few studies are devoted to the development of fundamental questions determining the main lines of development of analytical chemistry. The overwhelming majority of works are devoted to minor questions and often are inessential variations on topics that have long since been developed.

1. Determination of Solubility

One of the first applications of natural radioelements as indicators was the work of Hevesy and Paneth^50, devoted to determining the solubility of PbCrO₄ and PbS.

Modern methods of using radioactive isotopes for determining solubility are described in the article by A. N. Nesmeyanov^51. The idea of the method reduces to introducing a radioactive isotope into the compound under investigation, the specific activity \(q\) of the latter being determined. Then a small amount of this substance is kept for a long time at constant temperature in contact with the solvent. After equilibrium has been attained, a known volume of solvent is taken off and evaporated; the substance dissolved in this volume is collected in a cup or on a disk and subjected to measurement on a counter. If the volume of solvent taken is equal to \(v\), and the activity of the sample is \(a\), then the solubility of the substance may be calculated from the formula

\[ x=\frac{a}{vq}. \tag{6} \]

In a number of cases natural radioelements may be used as radioactive indicators. Thus V. Fomin, K. Zaborenko, and others^52,53, using ThB, determined the solubility of lead molybdate and iodide.

The possibilities of the method expanded considerably after artificial radioactivity had been discovered. At the present time we have at our disposal such a set of radioactive isotopes that they make it possible to apply the method considered by us to determining the solubility of practically any compound. As examples of the use of artificially radioactive isotopes for this purpose, we shall cite the work of V. I. Spitsyn and co-workers^54, devoted to determining the solubility of calcium molybdate with the aid of the isotope Mo^109. The method enabled the authors to determine the solubility of CaMoO₄ over a wide range of conditions and to show that the solubility in water has a maximum value at \(80^\circ\text{C}\), as is seen from consideration of Fig. 17, taken from the cited work.

APPLICATION OF RADIOACTIVE ISOTOPES IN ANALYTICAL CHEMISTRY

Volkov and Nesmeyanov[^55], using the isotope \(P^{32}\), determined the solubility of the salts \(\mathrm{BeNH_4PO_4H_2O}\) and \(\mathrm{Be_3(PO_4)_2}\) at various temperatures and various values of the hydrogen exponent.

As an example of work devoted to determining the solubility of liquids, we shall point to the study of Joris and Taylor[^56], who measured the solubility of water in benzene and other hydrocarbons. In this case they used tritium as the radioactive isotope.

In a number of foreign works devoted to determining the solubility of crystalline substances, solubility values are given almost exclusively in pure water. This entire cycle of works is difficult to apply to solving problems of analytical chemistry, since the solubility of precipitates obtained in analysis depends strongly on the ionic strength of the solution and on the individual chemical characteristics of the reagents present in the solution. This once again illustrates the proposition formulated above concerning the insufficient principled character and the absence of a synthetic approach in the scientific subject matter of scholars of capitalist countries. The first attempt to fill this gap was made by Neiman, Miller, and Fedoseev[^57]. They developed a rapid method for determining the solubility of analytical precipitates for the case when a large quantity of foreign ions is present in the solution. This method consists in precipitating the \(a\) millimoles of ions present in the solution, labeled with \(C\) microcuries of a radioactive isotope, by adding a precipitant, the volume of the solution being brought to \(v_1\) ml.

Fig. 17. Change in the solubility of calcium molybdate as a function of temperature.
Vertical axis: content of Mo in mg per 100 g of solution. Horizontal axis: temperature \((^\circ\mathrm{C})\).

The precipitate is filtered off, washed, and its activity \(I_1\) is determined with the aid of a counter. If the solubility of the precipitate is equal to \(x\ \mathrm{mmol}/\mathrm{ml}\), then \(xv_1\) will remain in the solution, and \((a - xv_1)\) millimoles of salt will be in the precipitate. It is clear that

\[ I_1 = c \frac{a - xv_1}{a}. \tag{7} \]

Next, another \(a\) millimoles of the nonradioactive substance under investigation are added to the solution and its secondary precipitation is carried out, the volume of the solution being brought to \(v_2\) ml.

It is easy to calculate that the activity of the second precipitate is

\[ I_2=\frac{cxv_1}{a}\cdot \frac{a+xv_1-xv_2}{a+xv_1}. \tag{8} \]

From (7) and (8) it follows that

\[ x=\frac{-a\sigma_1\beta+\sqrt{a^2\beta^2\sigma_1^2+4a^2\sigma_1\left[v_1+\beta(v_1-v_2)\right]}}{2v_1\left[v_1+\beta(v_1-v_2)\right]}. \tag{9} \]

Here \(\beta=\dfrac{I_1}{I_2}\).

If, by evaporating water, the volume of the solution in the secondary precipitation is brought to the initial volume, then \(v_2=v_1\), and formula (9) is considerably simplified. Under this condition

\[ x=\frac{a\left(\sqrt{\beta^2+4}-\beta\right)}{2v}. \tag{10} \]

The authors determined by this method the solubility of cuprous rhodanide and magnesium ammonium phosphate. The results of the determinations of the solubility of cuprous rhodanide are given in Table II.

Table II

Solubility of \(\mathrm{Cu_2(CNS)_2}\) in a \(\mathrm{ZnSO_4}\) solution
at \(20^\circ\mathrm{C}\)

As is seen from Table II, the probable error is approximately 10%. The solubility of \(\mathrm{Cu_2(CNS)_2}\) under the experimental conditions is \(0.46 \pm 0.05\) mmole/l.

2. Investigation of the Completeness of Precipitation, Adsorption, and Coprecipitation

The modern development of this branch of science is to a significant degree due to the classical works of Academician V. G. Khlopin, who developed, theoretically and experimentally, the questions of the distribution of a substance between a solution, a melt, and crystals, as well as the problems of adsorption of microcomponents\({}^{58}\).

These problems occupied V. G. Khlopin up to the last days of his life; he devoted to them a number of his last works[^59–^62]. Abroad, Fajans[^63] did much work on the study of the mechanism of coprecipitation and adsorption. The works of this investigator yielded a number of semi-theoretical rules that make it possible to predict the probability of coprecipitation and adsorption of natural radioactive elements present in negligible concentrations.

From the standpoint of analytical chemistry, works devoted to the investigation of coprecipitation and of the conditions for obtaining pure analytical precipitates are of considerably greater importance.

As an example of such investigations one may cite a series of works by Shvedov[^64–^66].

This author showed that, when calcium oxalate and magnesium ammonium phosphate are precipitated from solutions, considerable amounts of sodium are carried down into the precipitate. For the experiments the isotope Na[^24] was used; it was found that the precipitate CaC₂O₄ contains from 0.5 to 5 mg of sodium, and the precipitate MgNH₄PO₄—from 0.6 to 2.8 mg of sodium.

A number of similar works, considering particular cases of coprecipitation and adsorption, have been published abroad by Kolthoff[^67], Erbacher[^68], and others; however, in none of the published works was any attempt made to develop a general method of investigation and to give a general theory of coprecipitation. There is no doubt that this question, which is one of the key questions in modern analytical chemistry, must receive an exhaustive solution as a result of further investigations.

As was recently shown in the work of Miller, Neiman, and Sazonov[^69], labeled atoms can be used for a detailed study of the regularities of coprecipitation. The authors mentioned showed that, in the widely used method of precipitating barium in the form of BaCrO₄, coprecipitation of large amounts of strontium is observed. The authors carried out a number of experiments with mixtures of BaCl₂ and SrCl₂. The latter salt contained a small amount of the radioactive isotope Sr[^89]. Thus they were able to determine the weight of the precipitate obtained when barium was precipitated by chromic acid, and the content in this precipitate of SrCrO₄ from its radioactivity. From the filtrate, strontium was precipitated in the form of SrCO₃, which was converted into SrSO₄. The weight of the latter precipitate and its radioactivity were determined. These data made it possible to calculate the content of BaSO₄ in the precipitate. The data obtained are compared in Table III (see p. 116).

As is seen from the table, the first precipitate contains 6–8% strontium, and the second—up to 13% barium. Thus, the “good” results often obtained in gravimetric determinations are explained by the approximate compensation of the incompleteness of barium precipitation and the coprecipitation of strontium.

With the aid of the addition of the isotope Ba[^140] to the solution, a curve was obtained for the completeness of precipitation of BaCrO₄ as a function of the pH of the solution,

Table III

Weight and radiochemical determination data. Taken: 62.5 mg Ba and 51.6 mg Sr

and, by adding the isotope Sr\(^{89}\), the coprecipitation curves of SrCrO\(_4\) with changes in \(pH\) over wide limits. The results of the experiments are shown in Fig. 18. As can be seen from the figure, complete precipitation of barium is ensured in weakly acidic solutions with \(pH > 4\). Coprecipitation of strontium

Fig. 18. Coprecipitation of SrCrO\(_4\) with BaCrO\(_4\). All initial solutions contained \(2.46 \cdot 10^{-4}\) mol/l BaCl\(_3\) and different amounts of SrCl\(_2\): \(12.3 \cdot 10^{-4}\) mol/l (curve 2), \(2.51 \cdot 10^{-4}\) mol/l (curve 3), \(0.5 \cdot 10^{-4}\) mol/l (curve 4), and \(0.25 \cdot 10^{-4}\) mol/l (curve 5). Curve 1 shows the precipitation of BaCrO\(_4\) at different \(pH\) values, and curves 2–5 show the percentages of coprecipitated SrCrO\(_4\).

increases as the solution is neutralized and reaches a maximum at \(pH \simeq 7\). Therefore it is advisable to carry out the precipitation at such a \(pH\) that 100% precipitation of barium is ensured and a minimum of strontium coprecipitation is observed, i.e., at \(pH = 4.5\).

Having the data obtained, one can calculate the weight and composition of the first and second precipitates obtained at different \(pH\) values. The curves calculated in this way are shown in Fig. 19. As can be seen

Fig. 19. Dependence on \(pH\) of the weight of chromate precipitates (curve 1) and sulfates (curve 2) during the separation of barium and strontium.

from the figure, the experimental points representing the results of specially conducted experiments lie well on these curves, which testifies to the high accuracy of the results obtained by the radiochemical method.

The maxima of coprecipitation, clearly expressed on all the curves in Fig. 18, were explained by the authors by the fact that an intermediate stage in the cocrystallization of strontium is its adsorption on the surface of growing \(\mathrm{BaCrO_4}\) crystals. The rate of cocrystallization is inhibited in acidic and alkaline solutions by the adsorption of hydrogen or hydroxyl ions, reaching a maximum in neutral solutions.

The theory developed allowed the authors to put forward the supposition that the cocrystallization of strontium should be inhibited by surface-active substances.

The results of experiments carried out with the addition of 0.01% gelatin are shown in Fig. 20 (curve 3).

As can be seen from the figure, changing the order of addition of the reagents and adding gelatin decreased coprecipitation by approximately a factor of 6, which

made it possible, by dissolving the filtered precipitate and reprecipitating it, to obtain precipitates of \( \mathrm{BaCrO_4} \) practically free of strontium.

Fig. 20. Coprecipitation of strontium in the precipitation of \( \mathrm{BaCrO_4} \) according to Fresenius (curve 1), by the method of Neiman and co-workers (curve 2), and by the same method in the presence of 0.01% gelatin (curve 3).

There can be no doubt that the method of labeled atoms in the hands of Soviet scientists will yield many valuable results and will make it possible to improve modern methods of analysis considerably.

3. Extraction method

Recently, the method of separating substances by extraction with suitable solvents has found ever wider application in analytical chemistry. In developing this method as applied to specific systems, radioactive isotopes can greatly facilitate the solution of the problem. In developing in our laboratory a method for separating barium and strontium, the different solubility of \( \mathrm{SrBr_2} \) and \( \mathrm{BaBr_2} \) in isoamyl alcohol was used. Extraction of \( \mathrm{SrBr_2} \) was carried out in a Soxhlet apparatus, the completeness of the separation being determined with the aid of a counter. For this purpose, one of the isotopes \( \mathrm{Sr^{89}} \) or \( \mathrm{Ba^{140}} \) was first introduced into the mixture.

Preliminary experiments showed that \( \mathrm{SrBr_2} \) dissolves well in isoamyl alcohol, whereas \( \mathrm{BaBr_2} \) is practically insoluble. Therefore, by repeated extraction, it is possible to separate the mixture into practically pure \( \mathrm{BaBr_2} \) and \( \mathrm{SrBr_2} \). We followed the course of the separation with the aid of a counter. The experiments showed that, when the number of extractions is too small, a comparatively large amount of \( \mathrm{SrBr_2} \) remains in \( \mathrm{BaBr_2} \), which is evidently explained by the comparatively slow diffusion of the solution through the micropores.

On the other hand, with an excessively large number of extractions, noticeable amounts of BaBr₂ pass into the strontium salt. Radiometric control makes it possible quickly to determine the most advantageous number of extractions.

A method similar in conception for separating hafnium and zirconium by extracting them from a hydrochloric-acid aqueous solution with a benzene solution of thenoyltrifluoroacetone was developed by Huffman and Boffe⁷⁰. These authors determined the distribution coefficients of zirconium and hafnium when they were extracted from 2-N hydrochloric acid by solutions of thenoyltrifluoroacetone in benzene, while varying the concentration over wide limits.

In the chemistry of transuranium elements, a separation method based on the different solubilities of the salts of these metals in different valence states is widely used. In this case various solvents are employed in the presence of appropriately selected complexing agents⁷¹. In carrying out analyses of this kind there is no need to add labeled atoms, since all actinide isotopes are radioactive.

When the extraction method is applied to mixtures of nonradioactive elements, the method of adding labeled atoms makes it possible to simplify the control considerably. One of the first works in this field is that of Trehem and Siborg⁷², who used the radioisotope Cd¹⁰⁷ in developing a method for separating cadmium from cobalt by extraction with ether.

4. Stability of Complexes

For theoretical analytical chemistry, the dissociation constants of acids and complex compounds are of great importance. Knowledge of these quantities makes it possible to calculate the completeness of precipitation when various physicochemical parameters are changed. On the other hand, these same constants play a role in calculations of separation by the extraction method and by the method of partition chromatography.

Alongside potentiometric, polarographic, and spectrophotometric methods, in recent years the method of radioactive indicators has begun to be widely applied to the investigation of the stability of complexes.

The pioneer in this field was A. A. Grinberg, who more than 13 years ago developed a method for estimating the stability of complex ions from the rate of isotopic exchange of peripheral atoms and radicals with the ions of the complex-forming agent⁷³, ⁷⁴.

Grinberg’s method of studying the rate of isotopic exchange involving complex ions is currently being applied by a number of foreign researchers. As an example one may mention the extensive investigations by Adamson et al.⁷⁵ of the stability of a series of cyanide complexes of chromium, cobalt, iron, manganese, mercury, and molybdenum.

and nickel. In this work HCN labeled with the isotope \(C^{14}\) was used.

In a number of works, in studying the dissociation of complexes, additions of ion-exchange resins are used. By this method, for example, Schubert and Richter investigated the dissociation of barium citrate complexes\({}^{76}\).

As is evident from the brief review presented above, the labeled-atom method finds wide application in various branches of analytical chemistry.

Limiting ourselves to the examples cited above, we refer the reader interested in this field to review articles\({}^{77-79}\), in which additional material may be found.

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